R1ConsistentEstimator.java
package org.drip.measure.gamma;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>R1ConsistentEstimator</i> implements the Mixed Type Log-Moment Parameter Estimator for a Sequence of
* Observations. The References are:
*
* <br><br>
* <ul>
* <li>
* Devroye, L. (1986): <i>Non-Uniform Random Variate Generation</i> <b>Springer-Verlag</b> New York
* </li>
* <li>
* Gamma Distribution (2019): Gamma Distribution
* https://en.wikipedia.org/wiki/Chi-squared_distribution
* </li>
* <li>
* Louzada, F., P. L. Ramos, and E. Ramos (2019): A Note on Bias of Closed-Form Estimators for the
* Gamma Distribution Derived From Likelihood Equations <i>The American Statistician</i> <b>73
* (2)</b> 195-199
* </li>
* <li>
* Minka, T. (2002): Estimating a Gamma distribution https://tminka.github.io/papers/minka-gamma.pdf
* </li>
* <li>
* Ye, Z. S., and N. Chen (2017): Closed-Form Estimators for the Gamma Distribution Derived from
* Likelihood Equations <i>The American Statistician</i> <b>71 (2)</b> 177-181
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/gamma/README.md">R<sup>1</sup> Gamma Distribution Implementation/Properties</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class R1ConsistentEstimator
extends org.drip.measure.gamma.R1ParameterEstimator
{
/**
* Construct and Instance of R1ConsistentEstimator from the Array of Realizations
*
* @param realizationArray The Realization Array
*
* @return Instance of R1ConsistentEstimator
*/
public static final R1ConsistentEstimator FromRealizationArray (
final double[] realizationArray)
{
try
{
return new R1ConsistentEstimator (
new org.drip.validation.evidence.Sample (
realizationArray
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* R1ConsistentEstimator Constructor
*
* @param sample The Sample
*
* @throws java.lang.Exception Thrown of the Inputs are Invalid
*/
public R1ConsistentEstimator (
final org.drip.validation.evidence.Sample sample)
throws java.lang.Exception
{
super (
sample
);
}
/**
* Infer the Shape-Scale Parameter from the Observations
*
* @return The Shape-Scale Parameter from the Observations
*/
public org.drip.measure.gamma.ShapeScaleParameters inferShapeScaleParameter()
{
double[] realizationArray = sample().realizationArray();
int realizationCount = realizationArray.length;
double realizationLogRealizationSum = 0.;
double logRealizationSum = 0.;
double realizationSum = 0.;
for (int realizationIndex = 0;
realizationIndex < realizationCount;
++realizationIndex)
{
double logRealization = java.lang.Math.log (
realizationArray[realizationIndex]
);
logRealizationSum = logRealizationSum + logRealization;
realizationSum = realizationSum + realizationArray[realizationIndex];
realizationLogRealizationSum = realizationLogRealizationSum +
realizationArray[realizationIndex] * logRealization;
}
double nonNormalizedScale = realizationCount * realizationLogRealizationSum -
logRealizationSum * realizationSum;
try
{
return new org.drip.measure.gamma.ShapeScaleParameters (
realizationCount * realizationSum / nonNormalizedScale,
nonNormalizedScale / realizationCount / realizationCount
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Retrieve the Scale Bias Correction Factor
*
* @return The Scale Bias Correction Factor
*/
public double scaleBiasCorrectionFactor()
{
int realizationCount = sample().realizationArray().length;
return realizationCount / (realizationCount - 1);
}
/**
* Compute the Shape Bias Correction Adjustment
*
* @param scaleEstimate The Scale Estimate
*
* @return The Shape Bias Correction Adjustment
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double shapeBiasCorrectionAdjustment (
final double scaleEstimate)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
scaleEstimate
))
{
throw new java.lang.Exception (
"R1ConsistentEstimator::shapeBiasCorrectionAdjustment => Invalid Inputs"
);
}
double onePlusScaleEstimate = 1. + scaleEstimate;
return (3. * scaleEstimate
- (2. / 3. * scaleEstimate / onePlusScaleEstimate)
+ (4. / 5. * scaleEstimate / onePlusScaleEstimate / onePlusScaleEstimate)) /
sample().realizationArray().length;
}
}